Question

Each leg of a 45°-45°-90° triangle measures 12 cm. Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z X Y are 45 degrees. The lengths of sides Z Y and Y X are 12 centimeters. What is the length of the hypotenuse? 6 cm 6 StartRoot 2 EndRoot cm 12 cm 12 StartRoot 2 EndRoot cm

Answer 1

Answer:

Length of hypotenuse $12\sqrt2$ cm.

Step-by-step explanation:

We are given with a right angled triangle which has angles 45°-45°-90° and sides as 12 cm each.

Following labeling of dimensions is provided:

$\angle XYZ = 90^\circ\\\angle YZX = 45^\circ\\\angle ZXY = 45^\circ$

Sides:

ZY = 12 cm

YX = 12 cm

Please refer to the image attached as well.

To find: The hypotenuse, XZ = ?

It is well known that if the triangle is a right angled triangle, the pythagorean theorem holds well. As per the theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Height}^{2}$

Here, Base is ZY = 12 cm

Height, YZ = 12 cm

And Hypotenuse XZ is to be calculated.

Putting the values:

$XZ^2=12^2+12^2\\\Rightarrow XZ^2=144+144\\\Rightarrow XZ=\sqrt{144+144}\\\Rightarrow XZ=\sqrt{288}\\\Rightarrow XZ=12\sqrt{2}\ cm$

So, the answer is Hypotenuse, XZ = $12\sqrt{2}\ cm$.